January 11, 2021 Outline

Reading: text, §3.3
Due: Homework #1, due January 22; Project selection, due January 22

Module 10

1. Take-Grant Protection Model
   1. Counterpoint to HRU result
   2. Symmetry of take and grant rights
   3. Islands (maximal subject-only tg-connected subgraphs)
   4. Bridges (as a combination of terminal and initial spans)

2. Sharing
   1. Definition: can•share(α, x, y, G₀) true iff there exists a sequence of protection graphs G₀, …, G_n such that G₀ ⊢^* G_n using only take, grant, create, remove rules and in G_n, there is an edge from x to y labeled α
   2. Theorem: can•share(α, x, y, G₀) iff there is an edge from x to y labeled α in G₀, or all of the following hold:
      1. there is a vertex y′ with an edge from y′ to y labeled α;
      2. there is a subject y′′ which terminally spans to y′, or y′′ = y′;
      3. there is a subject x′ which initially spans to x, or x′ = x; and
      4. there is a sequence of islands I₁, …, I_n connected by bridges for which x′ ∈ I₁ and y′ ∈ I_n.
3. Model Interpretation
   1. ACM very general, broadly applicable; Take-Grant more specific, can model fewer situations
   2. Example: shared buffer managed by trusted third party

4. Stealing
   1. Definition: can•steal(α, x, y, G₀) true if, and only if, there is no edge from x to y labeled α in G₀, and there exists a sequence of protection graphs G₀, …, G_n for which the following hold simultaneously:
      1. There is an edge from x to y labeled α in G_n;
      2. There is a sequence of rule applications ρ₁ such that G_i−1 ⊢ G_i using ρ_i; and
      3. For all vertices v and w in G_i−1, 1 ≤ i < n, if there is an edge from v to y labeled α, then ρ_i is not of the form “v grants (α to y) to w”
   2. Theorem: can•steal(α, x, y, G₀) iff the following hold simultaneously:
      1. There is no edge from x to y labeled α in G₀;
      2. There exists a subject x′ such that x′ = x or x′ initially spans to x;
      3. There exists a vertex s with an edge labeled α to y in G₀; and
      4. can•share(t, x′, s, G₀) holds
5. Conspiracy
   1. What is of interest?
   2. Access, deletion sets
   3. Conspiracy graph
   4. Number of conspirators

Matt Bishop Office: 2209 Watershed Sciences Phone: +1 (530) 752-8060 Email: mabishop@ucdavis.edu

ECS 235B, Foundations of Computer and Information Security Version of January 10, 2021 at 4:04PM

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